Season pork with salt and pepper on all sides and set aside for 10 min. Next, whisk together the remaining marinade ingredients in a small bowl. Reserve 3 Tbsp. for basting. Pour the rest into food storage bag, add pork, seal and shake lightly to coat pork. Refrigerate for at least 30 min.
Meanwhile, roast tomatillos, shallots and apple in broiler until blistered and slightly blackened (8 to 10 min.) turning once. In small bowl, mix Mole Verde Spice, ¼ cup apple juice, 2 Tbsp. olive oil, 2 Tbsp. lime juice and ½ tsp. salt into a smooth paste. In food processor or blender, pulse mole paste, roasted ingredients and ¼ cup apple juice until thoroughly blended. Set aside.
Preheat oven to 400 degrees. Heat one Tbsp. of olive oil into a large saute pan over medium-high heat. Add pork and sear all sides until brown, 2 to 3 min. per side. Transfer to an uncovered baking dish and place in the oven for 17 min. to cook to medium. Baste twice during cooking with the reserved marinade. Remove and let rest for 10 min. before slicing. Meanwhile, over medium-high heat, add carrots to the same large saute pan and cook for 2 to 3 min. Next, add apple cider vinegar and deglaze the pan, scraping up any browned bits with a wooden spoon and reducing liquid by half. Add mole sauce, stir to coat carrots and cook for 2 to 3 min., stirring constantly. Stir in vegetable stock and remaining apple juice and bring to a boil. Reduce to a simmer, cover and cook for 5 to 6 min. In separate pan dry roast pecans until aromatic and lightly browned.
Serve along with rice sprinkled with pecans.